S1 Help - normal distribution.

Hey all.

The question Ive been doing is:

When a new fertiliser is used, the height of sunflowers follows a normal distribution with mean 115 cm. Given that 80% of the heights are now greater than 103 cm, find the standard deviation.

So I know P(X>103)=0.8.
And looking "outwards in" on the normal distribution table, z would equal to 0.842..

But according to the markscheme, z=-0.842 and I just really would like to know why it's a negative? Could anyone please help me in this?

It would be really really appreciated thanks :smile:

Reply 1

davidcy147

14

Right, you know that

Z=(X-mew)/Sigma

, so if you re-arrange in terms of sigma (standard deviation) solving will give you the answer.

(edited 14 years ago)

Reply 2

chridhe

OP

davidcy147

Right, you know that

Z=(X-mew)/Sigma

, so if you re-arrange in terms of sigma (standard deviation) solving will give you the answer.

no, i know that. :smile:

in the question,

(103 - 115) / sigma = z.

but to find sigma i need z, and to find z i had to use P(X>103) = 0.8. Looking backwards from the normal distribution, i found z = 0.842 when P(X>103) = 0.8.. but the answer shows z = -0.842 and i would just like to know why it's negative and not a positive number?

Reply 3

name0is0taken

1

As derived from the question 'P(X>103)=0.8, this when plotted on a normal distribution graph comes below the mean, hence the minus sign in 'z'

Reply 4

tamilGuy.

17

Original post by chridhe

Hey all.

The question Ive been doing is:

When a new fertiliser is used, the height of sunflowers follows a normal distribution with mean 115 cm. Given that 80% of the heights are now greater than 103 cm, find the standard deviation.

So I know P(X>103)=0.8.
And looking "outwards in" on the normal distribution table, z would equal to 0.842..

But according to the markscheme, z=-0.842 and I just really would like to know why it's a negative? Could anyone please help me in this?

It would be really really appreciated thanks :smile:

https://ibb.co/6nfvYjC

103 < 115. Below the mean, z must take negative values.